The Ocean-Atmosphere System
II: Oceanic Heat Budget
C. Chen
General Physical Oceanography
MAR 555
School for Marine Sciences and Technology
Umass-Dartmouth
MAR 555 Lecture 2: The Oceanic Heat Budget
Qs
Qb
Qh
Qv
Qe
Redistribute the heat
Qs: The short wave energy radiated from the sun (the shortwave radiation)
Qb: The net long-wave energy radiated back from the ocean (the longwave radiation);
Qe: The heat loss by evaporation (latent heat flux);
Qh: The sensible heat loss by conduction;
Qv: The heat transfer by currents (advection and convection)
Assuming that the ocean is a closed system, then the net heat flux at the sea
surface ΔQ equals to
!Q = Qs " Qb " Qe " Qh
Considering no global warming tendency, for a long-term averaging,
!Q = 0
QS = Qb + Qe + Qh
For a short-term, the net oceanic heat flux varies daily with diurnal variation
of solar radiation, etc. For the real ocean, due to the global warming,
!Q " 0
Question:
What are the physical processes controlling the heat flux?
Qs: The shortwave radiation (unit: W/m2)
Observational results:
Only 51% of the sun’s shortwave radiation energy can get onto the
sea surface:
51%
# 28% : directly from the sun after the reduction due to the cloud
$"
!23% : from sky radiation and longwave radiation of the atmosphere
S /4
!Tc4
Tc
!Tc4
!
S
4
Cloud layer
(1 " ! )
S
4
Sea surface
Total energy received at the sea surface is
QS = QS1 (direct ) + Qs2 (indirect ) = (1 # " )
S
+ !Tc4
4
The factors affecting Qs:
• The length of the day: varies with seasons and geographic latitude;
• The absorption of atmosphere (gas molecules, dust, water vapor);
• Effects of cloud: reduce the average amount of energy reaching the sea surface through
the absorption and scattering by the cloud)
Example 1:
Qs
Qs
Shortest path
a)
Minimum absorption
Longer path
b)
Larger absorption
Example 2:
Empirical equation:
QSC =
S
(1 ! 0.09c)
4
c: The proportion of cloud cover in the sky, which is estimated by an unit of eight divisions.
If the sky is completed covered by the cloud, c=8,
QSC =
S
S
S
(1 " 0.09c) = (1 " 0.09 ! 8) = 0.28
4
4
4
In the real ocean, the distribution of Qs varies with latitude. The annual
averaged values:
$< 150 & 200 W/m 2
!
QS = # 200 & 255 W/m 2
! < 200 W/m 2
"
' > 20 0 N
- 20 o S % ' % 20 o N
' < -20 o S
Annually averaged Qs(W/m2)
Question: Why is Qs larger on the continent than over the ocean?
Incoming solar radiation
(100 units)
Clear sky
Scattering back to space
(-7 units)
Absorption in upper atmosphere
by ozone
(-3 units)
Absorption in lower atmosphere by
water vapor and CO2
(-10 units)
80 units
Reflection from clouds
to space (-45 units)
Absorption in clouds
(-10 units)
25 units
Qb: The net long-wave radiation
All bodies with a temperature above absolute zero can emit radiation. The strength
of such an emission depends on body’s temperature: it is greater when the
temperature of the body is higher. Also, as the temperature of the body becomes
higher, the radiation spectrum is shifted toward shorter wavelengths.
In the real ocean, the energy emitted by the oceanic surface is estimated by a
black body with a sea-surface temperature Ts. The net upward longwave flux
Qb equals to the difference between sea and air longwave radiations, i.e.:
Qb = " (Ts4 ! Ta4 )
Ts: the water temperature at the sea surface
Ta: the air temperature at the sea surface
σ: Stenfan’s constant
Ta
Air
Ts
Sea
Sea surface
General evidences:
Small
•
Qb ~ 50 W /m2;
•
As the cloud coverage becomes larger, Qb decreases. However, Qb
doesn’t change much for ice and water;
•
Qb doesn’t change much either daily or seasonally because neither
sea temperature or relative humidity over the sea changes much in
these time scales.
•
(QS ! Qb ) water > (Qs ! Qb ) ice , (Qs ! Qb ) low
"Q = Qs ! Qb
Large "Q = Qs ! Qb
white
white
> (Qs ! Qb ) high latitude
Qs is small at high latitude and large at low latitude
Qb: does not change much with latitude
Equator
black
latitude
QS ! Qb
Qh: Sensible heat loss
1) The water is much denser than the air
# air ~ 1.2 " 1.3 kg/m 3 ,
# sea water ~ 1.025 ! 10 3 kg/m 3
so,
!sea water
!air
~ 10 3
The air-sea interface is very stable
if only the density difference is considered
However, the large temperature difference can cause a heat transfer from the warm
region to the cold region. Such a heat flux from the ocean is called sensible heat loss
or the heat loss by conduction.
Two conduction processes:
1) Molecular heat conduction; 2) Eddy (turbulent) diffusion
For the molecular case:
Qh = "c p k
!T
!z
k: the molecular conductivity of heat;
cp: the specific heat of the air at constant pressure
ΔT/Δz: the air temperature gradient at the sea surface
For the eddy case:
Qh = $ a c pa w#T # (= "c pa Az
!T
)
!z
w" and T " are turbulent fluctuation of vertical air velocity and temperaute
! a is the air density, and c pa is the specific heat of the dry air
Az is the vertical eddy viscosity.
Ta
Example:
a)
(high)
!T
> 0 , Qh < 0
!z
(low)
sea surface
The ocean gains heat
Ta
(low)
!T
< 0 , Qh > 0
!z
b)
high
The ocean losses heat
sea surface
Qe: The heat loss by evaporation (latent heat flux)
The latent heat flux can be estimated by a formula as
Qe = ! a Le w'q '
w! and q ' are turbulent fluctuation of vertical air velocity and water vapor mixing ratio.
Le is the latent heat of evaporation of the sea water, which can be estimated as
Le = (2.501 " 0.00237Ts ) ! 10 6 J/kg
In the real estimation,
Qe = ! a Le u* q*
u* and T* are the Monin - Obukhov similarity scaling parameters of the frictional velocity,
air temperature fluctuation.
Annual Latent Heat (W/m2)
Annual Sensible Heat (W/m2)
Heat flux measurements at the sea surface
Critical issues needed to be addressed in order to provide an accurate
estimation of Qe and Qh:
1)
Determine accurately u* under various stable or unstable conditions of the
thermal structure in the near-sea atmosphere boundary;
2)
Calculate accurately the air-sea temperature difference at the sea surface;
3)
Estimate the contribution of precipitation to the surface cooling
Issue 1): u* depends on the sea surface roughness and wind speed. How to calculate the
roughness and take convective velocity into account?
Issue 2): The air temperature is measured at a certain height above the sea surface from the
metrological buoys and ships, how to determine the true interfacial air-sea temperature
difference?
Issue 3): The true interfacial air-sea temperature difference is sensitively influenced by the
precipitation. Since the heavy rainfall usually companies with an atmospheric frontal
passages, how to determine its contribution to the surface cooling?
Observational evidences:
a)
The maximum Qe occurs on the west side of the ocean and winter because of the
existence of the west boundary warm current and large temperature gradient in
winter;
b)
At mid-latitude in the western North Pacific Ocean, Qe is about 145 W/m2. In the
western North Atlantic, Qe is about 195 W/m2;
c)
Qe and Qh are usually large during the storm passages.
Relation between Qe and Qh
In the ocean, Qh and Qe depends on the air-sea temperature difference and
wind speed at the sea surface. These two fluxes are correlated each other and
their relationship can be given as
Qh = RQe
Where R is the so-called Bowen’s ratio, which is equal to
R = 0.062(Ts ! Ta ) /(e s ! ea )
es and ea are the sea water saturated vapor pressure and actual air vapor pressure.
Question:
Is this relationship always valid?
Example:
Scatter plot of Qsen versus Qlat for February 3-7 nor’easter (dot) and August 1823 tropic storm Felix (diamonds), 1995 (Beardsley et al. 2003).
The Gulf of Maine Buoy Sites
Simulated
Assimilated
Short-wave
Long-wave
Latent
Sensible
Short-wave
Observed
Long-wave
SST
No SST
Latent
Sensible
The TOGA/COARE (TC) heat flux algorithm developed by Fairall et al. (1996):
•
•
•
•
More accurate skin water temperature;
Better paramterization of surface roughness;
More realistic vertical profiles for stable and unstable weather conditions
Accountable wind gustiness
Annual net surface heat flux (W/m2) averaged over 1978-2004
Annual longwave heat flux (W/m2) averaged over 1978-2004
Annual latent flux (W/m2) averaged over 1978-2004
Annual sensible flux (W/m2) averaged over 1978-2004
Suggested papers:
1)
Fairall, C. W., E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, 1996. Bulk
parameterization of air-sea fluxes for tropic ocean global atmosphere coupled-ocean
atmospheric response experiment. Journal of Geophysical Research, 101(C2), 3747-3764.
2)
Beardsley, R., S. Lentz, R. A. Weller, R. Limeburner, J. D. Irish, and J. B. Edson, 2003.
Surface forcing on the southern flank of Georges Bank, February-August, 1995. Journal of
Geophysical Research, 108, C11, 8007. Dot: 10.1029/2002JC001359.